A new metric is introduced which is suitable for estimating the rate of convergence of processes related to stable random variables. It is shown that it has an upper bound depending on the difference pseudomoments, but not on the absolute moments. This new metric is then applied to get some rates of convergence to a self-similar process constructed from a stable process.
Publié le : 1987-04-14
Classification:
Method of probability metrics,
ideal metric,
difference pseudomoment,
rate of convergence,
stable random variable,
self-similar process,
fractional stable process,
fractional calculus,
60E05,
60F05,
60E07,
60G50
@article{1176992167,
author = {Maejima, Makoto and Rachev, Svetlozar T.},
title = {An Ideal Metric and the Rate of Convergence to a Self-Similar Process},
journal = {Ann. Probab.},
volume = {15},
number = {4},
year = {1987},
pages = { 708-727},
language = {en},
url = {http://dml.mathdoc.fr/item/1176992167}
}
Maejima, Makoto; Rachev, Svetlozar T. An Ideal Metric and the Rate of Convergence to a Self-Similar Process. Ann. Probab., Tome 15 (1987) no. 4, pp. 708-727. http://gdmltest.u-ga.fr/item/1176992167/